Problem: As you very well know, this year's funkiest numbers are so called triangular numbers (that is, integers that are representable as <image>, where k is some positive integer), and the coolest numbers are those that are representable as a sum of two triangular numbers.

A well-known hipster Andrew adores everything funky and cool but unfortunately, he isn't good at maths. Given number n, help him define whether this number can be represented by a sum of two triangular numbers (not necessarily different)!

Input

The first input line contains an integer n (1 ≤ n ≤ 109).

Output

Print "YES" (without the quotes), if n can be represented as a sum of two triangular numbers, otherwise print "NO" (without the quotes).

Examples

Input

256


Output

YES


Input

512


Output

NO

Note

In the first sample number <image>.

In the second sample number 512 can not be represented as a sum of two triangular numbers.

Solution (in JAVA):

Solution:
import java.util.*;


public class CF121A {
    
    
    Scanner in = new Scanner(System.in);
    
    void run() {
        int n = in.nextInt();
        Set<Integer> nums = new TreeSet<Integer>();
        
        for (int i = 1, s = 0; s < 1000000000;) {
            s += (i++);
            nums.add(s);
        }
        
        for (Integer i : nums) {
            if (i >= n) {
                break;
            }
            
            if (nums.contains(n - i)) {
                System.out.println("YES");
                return;
            }
        }
        
        System.out.println("NO");
    }
    
    public static void main(String... args) {
        (new CF121A()).run();
    }
    
    
}